Strong stability for a fluid–structure interaction model

In this paper we consider the question of stabilization of a fluid–structure model that describes the interaction between a 3‐D incompressible fluid and a 2‐D plate, the interface, which coincides with a flat flexible part of the surface of the vessel containing the fluid. The mathematical model comprises the Stokes equations and the equations for the longitudinal deflections of the plate with inclusion of the shear stress, which the fluid exerts on the plate. We show that the energy associated with the model decays strongly when the interface is equipped with a locally supported dissipative mechanism. Our main tool is an abstract resolvent criterion due to Tomilov. Copyright © 2008 John Wiley & Sons, Ltd.